demodulation and decoding studies of the 39-tone mil-std ... · the signals were captured by the...

Demodulation and Decoding Studies of the 39-tone MIL-STD-188-110A HF Signal

Gerard Duprat

Defence R&D Canada - Ottawa TECHNICAL MEMORANDUM

DRDC Ottawa TM 2002-082 November 2002

Demodulation and decoding studies of the39-tone MIL-STD-188-110A HF signal

Gerard Duprat

Defence R&D Canada – OttawaTechnical Memorandum

DRDC Ottawa TM 2002-082

November 2002

Her Majesty the Queen as represented by the Minister of National Defence, 2002

Sa majeste la reine, representee par le ministre de la Defense nationale, 2002

Abstract

A set of algorithms has been developed to demodulate and decode the 39 tone signal,which is prevalent in the High Frequency (HF) frequency band. This signal, based onthe MIL-STD-188-110A Standard, is one of several different types generated by theAN/PRC-138 Harris radio. Defence R&D Canada (DRDC) - Ottawa has two of theseradios. Our work focused on the 39 tone fixed frequency mode, although the 39 tonesignal is also the underlying modulation used in the AN/PRC-138’s frequency hoppingmode. Thus, the work described here will also be useful to anyone developingdehopping and demodulation algorithms for the AN/PRC-138 frequency hoppingsignal. The signals were captured by the Agilent Technologies Blackbird system in alaboratory setting. The objective of the task was to gain a detailed understanding of thesophisticated 39 tone signal and to develop software radio algorithms for demodulatingand decoding the signal. The report describes the signal structure, the signal captureequipment, and the steps involved in demodulating and decoding the signal so that thetransmitted messages can be read at the receiving end. The report also describes theproblems encountered during the algorithm development process. Since the signalcaptures took place in an ideal setting anda priori information of the signal structurewas used to assist in the demodulation and decoding process, the current algorithmsmust be modified slightly to be able to handle the more general situation. The reportconcludes with ways of generalizing the algorithms.

Resum e

Un ensemble d’algorithmes aete concu afin de demoduler et de decoder les signauxcomposes de frequences multiples, utilisees simultanement (modema 39 tons, moded’operation parallele). Ce type de signal est utilise de facon preponderante dans labande de frequence HF. Ce signal est defini par le standard MIL-STD-188-110A. Lesradios de modele AN/PRC-138 manufacturees par Harris se servent de ce type designal, parmi tant d’autres, pour transmettre donnees et texte. Recherche etDeveloppement pour la Defense Canada (RDDC) - Ottawa possede deux de ces radios.Bien que durant la presenteetude l’accent soit mis seulement sur le mode d’operationdes radios en frequence fixe, il doitetre mentionne que les signauxa 39 tons sont aussiutilises par les radios AN/PRC-138 lorsqu’elles operent en mode bonds de frequence.Donc le travail decrit ici sera utilea toute personne qui voudra developper desalgorithmes dont le but est d’attacher ensemble les bonds d’une meme frequence ou dedemoduler les signaux transmis par les dites radios. Les signaux furent interceptes etrecueillis par le systeme Blackbird concu par Agilent Technologies. Le but de ce travailconsistaita acquerir une connaissance detaillee de ce genre de signal sophistique ainsique de developper un logiciel avec des algorithmes convenanta ce type de signal radio.Le rapport decrit la structure du signal, l’equipement utilise durant l’interception dessignaux, ainsi que les differentesetapes du processus de demodulation et de decodage.

DRDC Ottawa TM 2002-082 i

Ce processus aete mene jusqu’a son terme c’esta dire jusqu’au point ou un messagepeutetre lu. Le rapport decrit aussi les problemes rencontres durant le developpementdes algorithmes. Il y en eut beaucoup. Il doitetre mentionne que les signaux onteteinterceptes et recueillis dans des conditions ideales dans le laboratoire et en l’absencede tout bruit de fond. De plus, certaines caracteristiques de la structure du signal furentutiliseesa priori durant le processus de demodulation et de decodage. En consequence,ces algorithmes devrontetre legerement modifies afin d’etre utilises dans des conditionsplus generales et plus proche de la realite. Le rapport conclu avec des suggestions quirendront l’utilisation de ces algorithmes plus generale.

ii DRDC Ottawa TM 2002-082

Executive summary

The main objectives of the work described in this report were to gain a goodunderstanding of the signal generated by the 39 tone modem used in the HarrisAN/PRC-138 manpack radio, and to reach a stable point in the development ofsoftware radio algorithms used to demodulate and decode this signal. These goals wereachieved, making it possible to retrieve the content of a message which had beencaptured in a laboratory environment.

The work focused on the 39 tone fixed frequency mode of operation. However, the 39tone signal is also the underlying modulation used in the AN/PRC-138’s frequencyhopping mode. Thus, the work described here will also be extremely useful to anyonedeveloping dehopping and demodulation algorithms for the AN/PRC-138 frequencyhopping signal.

The 39 tone signal uses 39 subcarrier tones located in the audio frequency band. Eachtone is a Differential Quadrature Phase Shift Keyed (DQPSK) signal. A uniform baudrate of 44.44 symbols per second is used for all possible bit rates, which are 75, 150,300, 600, 1200, and 2400 bps. With this baud rate, the time duration of each symbol(symbol period or signal element) isTsymb = 22.5 ms. For bit rates less than 2400 bps,there will be some redundancy bits built into the signal. This is achieved with the timeand frequency diversity built into the signal structure. The lower the bit rate, the greaterthe redundancy.

At the start of a transmission, a preamble is used for synchronizing the receiving andtransmitting equipment, and for establishing a phase reference for subsequent signalelements (symbol periods). Periodically throughout the transmission, a synchronizationsignal is sent; this is accomplished through a framing process. The signal also has a40th tone added to it, which is unmodulated. This tone, also known as the Doppler orpilot tone, is used to correct frequency offsets introduced either by Doppler shifts in thesignal during transmission or by radio equipment instabilities.

The signal captures were carried out in an ideal laboratory environment. To handle amore general case, the current algorithms would have to be enhanced. Presently, timesynchronization of the data prior to demodulation is based on use of the preambletones. As mentioned in the report, a signal reception can occur anywhere during thetransmission, i.e., one might miss the preamble. If this is the case, any of the 39 tonescan be used for time synchronization purposes. This added capability in the algorithmswill require only a slight modification. Another problem is thata priori knowledge ofsome parameters were used for the deinterleaving and decoding activities (i.e., bit rateand interleaving degree); this information may not be readily available and, therefore,will have to be extracted in some way from the signal itself. Bit rate can be easilyidentified by looking at the redundancy within one signal element (for 2400 and 1200bps) and from the redundancy patterns existing between subsequent signal elements forbit rates below 1200 bps. Once the bit rate has been identified, the interleaving degreecan be deduced by determining the length in bits of the insertion interval between

DRDC Ottawa TM 2002-082 iii

framing sequence bits. Also, the decoding algorithms must be improved to be able tohandle the 2400 bps case which uses 56-bit codewords.

Finally, an area requiring more research is the problem of the rotation of the signalconstellations associated with each tone. It was speculated (but not proven) that thisrotation probably results from an offset in the spacing of the 39 tones.

Duprat, G. 2002. Demodulation and decoding studies of the 39-tone MIL-STD-188-110A HFsignal. DRDC Ottawa TM 2002-082. Defence R&D Canada – Ottawa.

iv DRDC Ottawa TM 2002-082

Sommaire

L’objectif premier du travail decrit dans ce rapport est d’acquerir une connaissancesolide du signal genere par le modema 39 tons utilise dans l’equipement portable radioAN/PRC-138 manufacture par Harris. Cet objectif inclut aussi la stabilisation desalgorithmes utilises pour demoduler et decoder ce type de signal. Ce but aete atteint. Ilfut possible de recuperer le contenu d’un messagea partir de donnees interceptees dansle laboratoire.

Bien que durant la presenteetude l’accent soit mis seulement sur le mode d’operationdes radios en frequence fixe, il doitetre mentionne que les signauxa 39 tons sont aussiutilises par les radios AN/PRC-138 lorsqu’elles operent en mode bonds de frequence.Donc le travail decrit ici sera utilea toute personne qui voudra developper desalgorithmes dont le but est d’attacher ensemble les bonds d’une meme frequence ou dedemoduler les signaux transmis par les dites radios.

Le signala 39 tons utilise 39 sous-porteuses localisees dans la bande de frequenceacoustique. Chaque ton (ou chaque sous-porteuse) est module differentiellement enquadrature par deplacement de phase (DQPSK). Un debit uniforme de 44.44 bauds (ousymboles par seconde) est utilise pour tous les debits binaires possibles. Avec un teldebit la duree de chaque symbole sera de 22.5 ms. Pour ce type de signal le debitbinaire ne peutetre que de 75, 150, 300, 600, 1200 ou 2400 bps. Pour les debitsinferieursa 2400 bps il y aura quelques symboles binaires (ou bits) redondant inclusdans le signal. Ceci est accompli gracea un processus de diversite en temps et enfrequence inclus dans la structure du signal. Plus le debit binaire sera faible, plus il yaura de bits superflus dans le signal.

Au debut de chaque transmission, un preambule est utilise afin de synchroniser lesequipementsemetteurs et recepteurs, ainsi que pour definir une valeur de reference pourla phase de chaque sous-porteuse. Durant la transmission un signal de synchronisationest envoye periodiquement. Il existe aussi dans le signal un quarantieme ton qui luin’est pas module. Ce ton est connu sous le non de ton Doppler (ou parfois ton pilote). Ilest utilise pour corriger les deviations en frequence causees dans le signal par l’effetDoppler ou bien par des instabilites propresa l’equipement radio.

Les signaux ontete interceptes et recueillis dans des conditions ideales dans lelaboratoire et en l’absence de tout bruit de fond. En consequence, ces algorithmesdevrontetre modifies afin d’etre utilises dans des conditions plus generales et plusproche de la realite. Actuellement la synchronisation en temps des donnees, necessairepour obtenir une demodulation exacte, est accomplie en utilisant les caracteristiquesdes sous-porteuse durant le preambule. Il estevident qu’un signal peutetre intercepte etrecu n’importe quand durant la transmission. Il est donc possible que le preambule nesoit pas intercepte. Dans ce cas, n’importe laquelle des 39 sous-porteuses, existant dansun symbole, peutetre utilisee pour synchroniser les donnees en temps. Modifier lesalgorithmes en ce sens sera simple. Un autre probleme reside dans le fait qu’uneconnaissancea priori de certain parametres est utilisee notamment pour demeler et

DRDC Ottawa TM 2002-082 v

regrouper ainsi que pour decoder les donnees (par exemple le debit binaire et le degrede fragmentation). Cette information peut ne pasetre accessible directement et doncdoit etre extraite du signal lui-meme. Le debit binaire est facilement identifiable enobservant le patron (la structure) des bits redondantsa l’interieur de chaque symbole etaussi comment ce patron varie d’un symbolea l’autre. Une fois le debit binaireetabli,le degre de fragmentation sera trouve en determinant la longueur des donnees, en bit,existant entre deux sequences consecutives de synchronisation.

Pour finir, la cause de la rotation observee dans la constellation du signal et qui dependde la frequence de chaque sous-porteuse devraetre investiguee. Il aete suggere (maisnon formellement prouve) que cette rotationetait probablement causee par un legerdesaccord existant dans le taux d’echantillonnage entre les radios et l’equipementutilise pour intercepter le signal. Ceci fait que les 39 sous-porteuses ne sont pasexactement separees par 56.25 Hz tel qu’indique dans le standard MIL-STD-188-110A.

Duprat, G. 2002. Demodulation and decoding studies of the 39-tone MIL-STD-188-110A HFsignal. DRDC Ottawa TM 2002-082. R&D pour la defense Canada – Ottawa.

vi DRDC Ottawa TM 2002-082

Table of contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Resume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Executive summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Sommaire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Table of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

List of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

List of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2. OVERVIEW OF THE 39-TONE MODEM SIGNAL . . . . . . . . . . . . . . . 1

2.1 General Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2.2 Signal Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.3 Encoding and Decoding . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.1 Reed-Solomon Codes . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.2 Galois Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.3 RS Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.4 Decoding RS codes . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4 Extracting the Data Bits . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3. EXPERIMENTAL SET-UP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4. DEMODULATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.1 Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.2 Phase Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5. DEINTERLEAVING AND DECODING . . . . . . . . . . . . . . . . . . . . . . 44

6. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

DRDC Ottawa TM 2002-082 vii

List of figures

1 Message generating process using the 39 tone modem. . . . . . . . . . . . . . . 2

2 Spectrum structure of the 39 tone signal. . . . . . . . . . . . . . . . . . . . . . . 3

3 Signal structure of the 39 tone waveform. . . . . . . . . . . . . . . . . . . . . . 3

4 Shift register configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

5 Signal constellation for the DQPSK modulation on each tone. . . . . . . . . . . 7

6 Interleaver for an even number of code words. . . . . . . . . . . . . . . . . . . . 9

7 Interleaver for an odd number of code words. . . . . . . . . . . . . . . . . . . . 9

8 Portion of the time domain 39 tone signal. . . . . . . . . . . . . . . . . . . . . . 25

9 Power spectral density of part one of the preamble. . . . . . . . . . . . . . . . . 26

10 Power spectral density of part two of the preamble. . . . . . . . . . . . . . . . . 27

11 Power spectral density of part one of the preamble after frequencysynchronization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

12 Time synchronization process. . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

13 Phase difference during time synchronization process. . . . . . . . . . . . . . . 31

14 Spectrum when data are synchronized in time. . . . . . . . . . . . . . . . . . . . 32

15 Spectrum when time synchronization is not perfectly achieved. . . . . . . . . . . 33

16 Spectrum when there is no time synchronization whatsoever. . . . . . . . . . . . 34

17 Spectrum of 39 tone waveform. . . . . . . . . . . . . . . . . . . . . . . . . . . 35

18 Spectrum of 39 tone waveform after time and frequency synchronization. . . . . 37

19 Successive phase differences from symbol period to symbol period for tonenumber 1 over a duration of 30 symbol periods. . . . . . . . . . . . . . . . . . . 38

20 Signal constellation for tone number one over 703 symbol periods. . . . . . . . . 39

21 Signal constellation for tone number 10 over 703 symbol periods. . . . . . . . . 40

22 Signal constellation for tone number one over 703 symbol periods afterconstellation rotation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

viii DRDC Ottawa TM 2002-082

23 Signal constellation for tone number 10 over 703 symbol periods afterconstellation rotation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

24 End sequence for first framing sequence . . . . . . . . . . . . . . . . . . . . . . 43

25 Deinterleaving and decoding process. . . . . . . . . . . . . . . . . . . . . . . . 45

DRDC Ottawa TM 2002-082 ix

List of tables

1 Normalized Amplitudes and Phases for Tones . . . . . . . . . . . . . . . . . . . 4

2 Framing Sequence Insertion Intervals and Lengths . . . . . . . . . . . . . . . . . 6

3 Time/Frequency Diversity at 75 bps . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Time/Frequency Diversity at 150 bps . . . . . . . . . . . . . . . . . . . . . . . . 12



7 Time/Frequency Diversity at 1200 bps . . . . . . . . . . . . . . . . . . . . . . . 15

8 Time/Frequency Diversity at 2400 bps . . . . . . . . . . . . . . . . . . . . . . . 16

9 Elements ofGF (24) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

10 Example of Decoded Bit Stream . . . . . . . . . . . . . . . . . . . . . . . . . . 47

x DRDC Ottawa TM 2002-082

1. INTRODUCTION

A set of algorithms have been developed to demodulate and decode the 39 tone signal,based on the MIL-STD-188-110A standard. The 39 tone signal is found in the HFfrequency band and is one of several different types (including Automatic LinkEstablishment (ALE) and Frequency Hopping) used by two Harris AN/PRC-138manpack radios purchased by DRDC Ottawa for experimental purposes. The 39 tonesignal is the underlying modulation used in the AN/PRC-138’s frequency hoppingmode. Thus, this work will be very useful to anyone developing dehopping anddemodulation algorithms for the AN/PRC-138 frequency hopping signal. Our work,however, focused on the the 39 tone fixed frequency mode.

The signals were captured using an Agilent Blackbird system in a laboratory setting.The objective of the task was to gain a detailed understanding of this complex signal sothat demodulation and decoding algorithms could be developed. This report describesthe details of the signal structure, the signal capture equipment, and the steps involvedin demodulating and decoding the signal. The algorithms have been developed so thatthe transmitted message can be read at the receiving end. The problems encounteredduring the algorithm development process are also described. Since the signal capturestook place in an ideal setting, anda priori information of the signal structure was usedto assist in the demodulation and decoding process, the current algorithms would needto be modified slightly to handle a more general situation. Therefore this reportconcludes with methods for carrying out these generalizations.

2. OVERVIEW OF THE 39-TONE MODEM SIGNAL

This section presents the general concepts associated with the 39 tone signal, the detailsof the signal structure, issues related to encoding and decoding the data, and finally thesteps involved in extracting the data bits from the received signal. The contents of thissection are based on information provided in [1].

2.1 General Concepts

The 39 tone signal uses 39 subcarrier tones located in the audio frequency band. Eachtone is a Differential Quadrature Phase Shift Keyed (DQPSK) signal. A uniform baudrate of 44.44 symbols per second is used for all possible bit rates, which are 75, 150,300, 600, 1200, and 2400 bps. With this baud rate, the time duration of each symbol(symbol period or signal element) isTsymb = 22.5 ms. For bit rates less than 2400 bps,there will be some redundancy bits built into the signal, the redundancy increasing asthe bit rate decreases. This will be shown in more detail later.

At the start of a transmission, a preamble is used for synchronizing the receiving andtransmitting equipment, and for establishing a phase reference for subsequent signalelements (symbol periods). Periodically throughout the transmission, a synchronization

DRDC Ottawa TM 2002-082 1

signal is sent; this is accomplished through a framing process. The signal also has a40th tone added to it, which is unmodulated. This tone, also known as the Doppler orpilot tone, is used to correct frequency offsets introduced either by Doppler shifts in thesignal during transmission, or by radio equipment instabilities.

The process of generating the overall signal at baseband is illustrated in Figures 1 and2. Given a sequence of bits, the signal is constructed in the digital frequency domain. Ablock of bits corresponding to a symbol period is mapped onto the 39 tones, where eachtone (which represents 2 bits during that symbol period) will have a phasecorresponding to the 2-bit symbol. Once the signal in the frequency domain isconstructed in this fashion for that symbol period, the Doppler tone is then added. Atthat point, the frequency domain signal is converted to a sampled signal in the timedomain using the inverse Fast Fourier Transform (FFT). The sampled signal is thenapplied to a D/A converter. The resulting analog baseband signal is used to modulate aSingle Sideband (SSB) signal at Radio Frequency (RF).

7 bit ASCII Text

Convert to 10 bit Words

Reed Solomon

FEC Interleave Add Block

Synch

Generate Symbols

Map to 39 Tones

Add Doppler

Tone

Inverse FFT

D/A Converter

Bit Stream

10 11 10 -------- 00 Tone

1 Tone

2 Tone

3 Tone

39

11 11 01 -------- 10 Tone

1 Tone

2 Tone

3 Tone

39

n T symb ( n + 1 ) T symb

101110--------00111101--------10

Figure 1: Message generating process using the 39 tone modem.

The task of the Electronic Support Measures (ESM) operator, given an SSB 39 tonesignal that has been received at RF, is to work backwards. The operator must tune theESM receiver onto the signal, mix it to baseband where it is digitized, attempt tosynchronize to the signal in time and frequency, obtain a sequence of symbols bymeasuring the phase difference from symbol period to symbol period, convert thesymbol sequence into a serial bit stream, and perform bit deinterleaving and ForwardError Correction (FEC) decoding. The process of accomplishing this will be discussedin the subsequent paragraphs.

2 DRDC Ottawa TM 2002-082

Doppler Tone 7 D f =

393.75 Hz

D f = 56.25 Hz

Tone 1 12 D f = 675 Hz

Tone 39 50 D f =

2812.5 Hz

63 D f = 3543.75 Hz

- 64 D f = -3600 Hz

D f = 56.25 Hz

Figure 2: Spectrum structure of the 39 tone signal.

2.2 Signal Structure

The sequence of events occurring during the transmission phase is illustrated inFigure 3. From this figure, it can be seen that the signal is composed of a preamble,synchronization blocks, and data blocks.

Prior to transmission of the data, a three-part preamble is transmitted. The first part ofthe preamble is 14 signal elements (symbol periods) long, and consists of fourequal-amplitude unmodulated data tones of 787.5, 1462.5, 2137.5 and 2812.5 Hz. Parttwo of the preamble is 8 signal elements long and consists of three modulated datatones of 1125.0, 1800.0 and 2475.0 Hz. These tones are advanced byπ radians at thebeginning of each signal element of the second part of the preamble. The third part ofthe preamble is one signal element in duration and consists of all 39 tones (56.25 Hzapart) plus the Doppler tone. This part of the preamble establishes the starting phasereference for subsequent signal elements. The tone phases at the onset of each part ofthe preamble, along with their normalized amplitudes, are described in Table 1.

4 Unmodulated Tones

3 Modulated Tones

Block Sync

Data Super Block(s) 1 - 576 Blocks

8064 to 31752 bits

Block Sync

Fill or

Data

Data Async EOM

517.5 ms

315 ms 180 ms 22.5 ms

Preamble 40 Reference Tones

14 Symbol Periods

8 Symbol Periods

( 1 Symbol Period )

Figure 3: Signal structure of the 39 tone waveform.


Table 1: Normalized Amplitudes and Phases for Tones

Preamble Part Tone Frequency (Hz) Tone Function Amplitude Initial Phase (Deg)

1 787.50 Data Tone 3 3 0.01 1462.50 Data Tone 15 3 103.71 2137.50 Data Tone 27 3 103.71 2812.50 Data Tone 39 3 0.02 1125.00 Data Tone 9 4 0.02 1800.00 Data Tone 21 4 90.02 2475 Data Tone 33 4 0.03 393.75 Doppler Tone 2 0.03 675.00 Data Tone 1 1 0.03 731.25 Data Tone 2 1 5.63 787.50 Data Tone3 1 19.73 843.75 Data Tone 4 1 42.23 900.00 Data Tone 5 1 73.13 956.25 Data Tone 6 1 115.33 1012.50 Data Tone 7 1 165.93 1068.75 Data Tone 8 1 225.03 1125.00 Data Tone 9 1 295.33 1181.25 Data Tone 10 1 14.13 1237.5 Data Tone 11 1 101.33 1293.75 Data Tone 12 1 199.73 1350.00 Data Tone 13 1 303.83 1406.25 Data Tone 14 1 59.13 1462.50 Data Tone 15 1 185.63 1518.75 Data Tone 16 1 317.83 1575.00 Data Tone 17 1 101.33 1631.25 Data Tone 18 1 253.13 1687.50 Data Tone 19 1 56.33 1743.75 Data Tone 20 1 225.03 1800.00 Data Tone 21 1 45.03 1856.25 Data Tone 22 1 236.33 1912.50 Data Tone 23 1 73.13 1968.75 Data Tone 24 1 281.33 2025.00 Data Tone 25 1 137.83 2081.25 Data Tone 26 1 5.63 2137.50 Data Tone 27 1 239.13 2193.75 Data Tone 28 1 123.83 2250.00 Data Tone 29 1 19.73 2306.25 Data Tone 30 1 281.33 2362.50 Data Tone 31 1 194.13 2418.75 Data Tone 32 1 115.3


Preamble Part Tone Frequency (Hz) Tone Function Amplitude Initial Phase (Deg)

3 2475.00 Data Tone 33 1 45.03 2531.25 Data Tone 34 1 345.93 2587.50 Data Tone 35 1 295.33 2643.75 Data Tone 36 1 253.13 2700.00 Data Tone 37 1 222.23 2756.25 Data Tone 38 1 199.73 2812.50 Data Tone 39 1 185.6

Block synchronization, which controls the framing process, enables the location of thedata block (also referred to as superblocks) boundaries. This synchronization mustoccur before proper deinterleaving and decoding can commence. Framing isestablished by periodically inserting a known pseudorandom sequence into the encodeddata bit stream. The pseudorandom sequence is generated by the primitive polynomialf(x) = x9 + x7 + x6 + x4 + 1. The feedback register to generate the sequence isillustrated in Figure 4. The block framing sequence is inserted every time a specificnumber of superblocks has been transmitted; the actual number can be found in [1].The length of the framing sequence is predefined and varies with the data rate and theinterleaving degree, also specified in [1]. The insertion interval (the number of bitsbetween framing sequence bits), the framing sequence length and the interleavingdegree depend on the transmission mode: synchronous or asynchronous. In theasynchronous case, these parameters also depend on the number of bits used to formthe character set. To illustrate this point, Table 2 provides the various combinations ofinsertion interval, sequence length and interleaving degree for the 10-bit asynchronouscharacter set used by the radio in this study. Other combinations can be found in [1]. Itshould be noted that the final sequence of bits of the framing sequence is always1111111110.

Framing Sequence

x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 x 0

Figure 4: Shift register configuration.

Following the block synchronization are the data blocks, or superblocks. The bit streamforming the data blocks results from the demodulation of the 39 tone waveform. Tonefrequencies and normalized amplitudes are as indicated in Table 1. All the data tones, intheory, maintain constant amplitude. The amplitude of the Doppler tone is 6 dB higherthan the amplitude of the other tones. The 39 tones are simultaneously keyed to producea 22.5 ms long signal element for each tone. At the onset of each signal element, every


Table 2: Framing Sequence Insertion Intervals and Lengths

Data Rate (bps) Interleaving Insertion Insertion SequenceDegree Interval Interval Length

(Superblocks) (bits) (bits)75 1 585 16380 26075 4 242 27104 41675 12 75 25200 40075 35 18 17640 280150 1 585 16380 260150 9 110 27720 440150 25 36 25200 400150 75 9 18900 300300 1 585 16380 260300 17 49 23324 356300 47 22 27720 440300 153 5 21420 340600 1 585 16380 260600 33 30 27720 440600 99 10 27720 440600 315 2 17640 2801200 1 585 16380 2601200 63 15 26460 4201200 195 6 32760 5201200 585 1 16380 2602400 1 144 13440 2562400 36 7 23520 4482400 72 3 20160 3842400 288 1 26880 512


data tone experiences a phase advance relative to its phase at the start of the previoussignal element. Four values are allowed for a phase change: 45, 135, 225, or 315degrees. For each signal element the 39 phase changes are mapped into a 2-bit symbol(also called a di-bit). This results in a stream of 78 bits. The mapping, illustrated inFigure 5, is as follows:45◦ → 10, 135◦ → 00, 225◦ → 01, and315◦ → 11.

I

Q

π/4 3π/4

5π/4 7π/4

DQPSK

01 00

10 11

Example: A bit sequence of 01 01 01 01 on a particular tone maps into the symbol sequence:

exp[ j( ref + π /4 ) ] exp[ j( ref + π /2 ) ] exp[ j( ref + 3 π /4 ) ] exp[ j( ref + 2 π ) ]

where " ref " is the initial phase of the tone prior to the transmission of the bit sequence.

Figure 5: Signal constellation for the DQPSK modulation on each tone.

There is certain amount of redundancy in the data transmitted within one signalelement, which depends on the bit rate. For bit rates less than 2400 bps, informationcarried on tones 1 through 7 (bits 1 to 14) is also carried on tones 33 through 39 (bits 65to 78). In addition, the first 64 bits of the 78 bit block are partitioned into a number ofdata words to be transmitted during each 22.5 ms signal element. The number of datawords depends on the bit rate. For all the applicable bit rates, the bit stream for onesignal element is organized as follows:

(a) Maximum redundancy exists at 75 bps. Sixteen 4-bit long data words ofinformation are carried in bits 1 to 64, with bits 65 to 78 carrying theinformation already in bits 1 to 14.

(b) Full redundancy exists at 150 bps. Eight 8-bit long data words of theinformation are carried in bits 1 to 64, with bits 65 to 78 carrying theinformation already in bits 1 to 14.


(c) Full redundancy exists at 300 bps. Four 16-bit long data words ofinformation are carried in bits 1 to 64, with bits 65 to 78 carrying theinformation already in bits 1 to 14.

(d) Full redundancy at 600 bps. Two 32-bit long data words of information arecarried in bits 1 to 64, with bits 65 to 78 carrying the information alreadyin bits 1 to 14.

(e)Partial redundancy exists at 1200 bps. One 64-bit data word of informationis carried in bits 1 to 64, with bits 65 to 78 carrying the information alreadyin bits 1 to 14.

(f) No redundancy at 2400 bps. One 78-bit long data word carries theinformation.

Only the first data word in the 78-bit stream contains current information (the amountof current information depends on the bit rate; for example, 150 bps implies data wordsizes of 8 bits). The other subsequent data words of the 78-bit stream are copies of datawords already transmitted during previous signal elements. Tables 3 to 8 illustrate thistime/frequency diversity structure for each of the available bit rates.

Once the tones have been translated into a bit stream, the data is deinterleaved and thendecoded. From the ESM perspective, we are only interested in the deinterleavingprocess. However, to better understand this process, the interleaving at the transmitterwill be briefly described.

There are four possible interleaving degrees for bit rates under 2400 bps. At 2400 bps,there are eight interleaving degrees. The various interleaving degrees are listed inTable 2. The interleaver takes the input of an FEC encoded data block and creates asingle bit stream by sending the data bits row by row. Figures 6 and 7 illustrate theinterleaving process.

Deinterleaving is the reverse operation. The actual deinterleaving process is carried outas follows:

(a) Isolate all the data bits delimited by two synchronization blocks.

(b) Group the data bits into superblocks, where each superblock containsxnbits, wherex is the interleaving degree andn is the length of a codeword.The code words are 28 bits long (12 data bits and 16 parity bits) for bitrates below 2400 bps, and 56 bits long (40 data bits and 16 parity bits) for2400 bps.

(c) Split the superblocks into codewords as illustrated in Figures 6 and 7.

(d) Input the codewords into the decoder. The encoding/decoding process isbased on 4-bit long symbols. From Figures 6 and 7 it can be seen that someinterleaving occurs in the encoder for the 28-bit long codewords. Thesecodewords are created in pairs. The 4-bit symbols are created two at a time.


D0 D1 D2 D3 D4 D5 D6 D7

D8 D9 D10 D11 D12 D13 D14 D15

D16 D17 D18 D19 D20 D21 D22 D23

D24 D25 D26 D27 D28 D29 D30 D31

D32 D33 D34 D35 D36 D37 D38 D39

D40 D41 D42 D43 D44 D45 D46 D47

P0 P1 P2 P3

P4 P5 P6 P7

P8 P9 P10 P11

P12 P13 P14 P15

P16 P17 P18 P19

P20 P21 P22 P23

P24 P25 P26 P27

P28 P29 P30 P31

P32 P33 P34 P35

P36 P37 P38 P39

P40 P41 P42 P43

P44 P45 P46 P47

P48 P49 P50 P51

P52 P53 P54 P55

P56 P57 P58 P59

P60 P61 P62 P63

Symbol 0

Symbol 1

Symbol 2

Symbol 3

Symbol 4

Symbol 5

Symbol 6

Data Symbols

Parity Symbols

Codeword 1 Codeword 2 Codeword 3 Codeword 4

FEC Encoder

Interleaver D47 D46 D45 D44 ... D4 D3 D2 D1 D0

P15 P14 ... P1 P0 D19 D18 D17 D16 D11 D10 D9 D8 D3 D2 D1 D0

Codeword 1

First Bit In

First Bit Out

P63 P62 ... P12 ... P1 D47 .... D16 D39 ... D8 D31 D30 D29 D28 D27 D26 D25 D24 D7 D6 D5 D4 D3 D2 D1 D0

First Bit Out

Output of Interleaver

Figure 6: Interleaver for an even number of code words.

D0 D1 D2 D3 D4 D5 D6 D7

D8 D9 D10 D11 D12 D13 D14 D15

D16 D17 D18 D19 D20 D21 D22 D23

D24 D25 D26 D27

D28 D29 D30 D31

D32 D33 D34 D35

P0 P1 P2 P3

P4 P5 P6 P7

P8 P9 P10 P11

P12 P13 P14 P15

P16 P17 P18 P19

P20 P21 P22 P23

P24 P25 P26 P27

P28 P29 P30 P31

P32 P33 P34 P35

P36 P37 P38 P39

P40 P41 P42 P43

P44 P45 P46 P47

Symbol 0

Symbol 1

Symbol 2

Symbol 3

Symbol 4

Symbol 5

Symbol 6

Data Symbols

Parity Symbols

Codeword 1 Codeword 2 Codeword 3

FEC Encoder

Interleaver D35 D34 ... D4 D3 D2 D1 D0

P15 P14 ... P1 P0 D19 D18 D17 D16 D11 D10 D9 D8 D3 D2 D1 D0

Codeword 1

First Bit In

First Bit Out

P47 P46 ... P12 ... P1 D35 ... D16 D31 ... D12 D11 D10 D9 D8 D27 D26 D25 D24 D7 D6 D5 D4 D3 D2 D1 D0

First Bit Out

Output of Interleaver

Figure 7: Interleaver for an odd number of code words.


The first 4 bits into the encoder form the first symbol in the first codeword.The next 4 bits form the first symbol in the second codeword, etc. After apair of codewords is created in the encoder, they are stacked together withthe other codewords for that sequence and then put into the interleaver.


Table 3: Time/Frequency Diversity at 75 bps

Tone Number Bit Number Data Word1 1 2 Actual Word2 3 43 1 2 Copy of word transmitted 14 3 4 signal element in the past5 1 2 Copy of word transmitted 26 3 4 signal elements in the past7 1 2 Copy of word transmitted 38 3 4 signal elements in the past9 1 2 Copy of word transmitted 410 3 4 signal elements in the past11 1 2 Copy of word transmitted 512 3 4 signal elements in the past13 1 2 Copy of word transmitted 614 3 4 signal elements in the past15 1 2 Copy of word transmitted 716 3 4 signal elements in the past17 1 2 Copy of word transmitted 818 3 4 signal elements in the past19 1 2 Copy of word transmitted 920 3 4 signal elements in the past21 1 2 Copy of word transmitted 1022 3 4 signal elements in the past23 1 2 Copy of word transmitted 1124 3 4 signal elements in the past25 1 2 Copy of word transmitted 1226 3 4 signal elements in the past27 1 2 Copy of word transmitted 1328 3 4 signal elements in the past29 1 2 Copy of word transmitted 1430 3 4 signal elements in the past31 1 2 Copy of word transmitted 1532 3 4 signal elements in the past33 1 2 Copy of actual word34 3 435 1 2 Copy of word transmitted 136 3 4 signal element in the past37 1 2 Copy of word transmitted 238 3 4 signal elements in the past39 1 2 Partial copy of word 3 elements

in the past



Tone Number Bit Number Data Word1 1 2 Actual Word2 3 43 5 64 7 85 1 2 Copy of word transmitted 26 3 4 signal elements in the past7 5 68 7 89 1 2 Copy of word transmitted 410 3 4 signal elements in the past11 5 612 7 813 1 2 Copy of word transmitted 614 3 4 signal elements in the past15 5 616 7 817 1 2 Copy of word transmitted 818 3 4 signal elements in the past19 5 620 7 821 1 2 Copy of word transmitted 1022 3 4 signal elements in the past23 5 624 7 825 1 2 Copy of word transmitted 1226 3 4 signal elements in the past27 5 628 7 829 1 2 Copy of word transmitted 1430 3 4 signal elements in the past31 5 632 7 833 1 2 Copy of actual word34 3 435 5 636 7 837 1 2 Partial copy of word38 3 4 transmitted 2 elements39 5 6 in the past



Tone Number Bit Number Data Word1 1 2 Actual Word2 3 43 5 64 7 85 9 106 11 127 13 148 15 169 1 2 Copy of word transmitted 410 3 4 signal elements in the past11 5 612 7 813 9 1014 11 1215 13 1416 15 1617 1 2 Copy of word transmitted 818 3 4 signal elements in the past19 5 620 7 821 9 1022 11 1223 13 1424 15 1625 1 2 Copy of word transmitted 1226 3 4 signal elements in the past27 5 628 7 829 9 1030 11 1231 13 1432 15 1633 1 2 Partial copy of actual word34 3 435 5 636 7 837 9 1038 11 1239 13 14



Tone Number Bit Number Data Word1 1 2 Actual Word2 3 43 5 64 7 85 9 106 11 127 13 148 15 169 17 1810 19 2011 21 2212 23 2413 25 2614 27 2815 29 3016 31 3217 1 2 Copy of word transmitted 818 3 4 signal elements in the past19 5 620 7 821 9 1022 11 1223 13 1424 15 1625 17 1826 19 2027 21 2228 23 2429 25 2630 27 2831 29 3032 31 3233 1 2 Partial copy of actual word34 3 435 5 636 7 837 9 1038 11 1239 13 14



Tone Number Bit Number Data Word1 1 2 Actual Word2 3 43 5 64 7 85 9 106 11 127 13 148 15 169 17 1810 19 2011 21 2212 23 2413 25 2614 27 2815 29 3016 31 3217 33 3418 35 3619 37 3820 39 4021 41 4222 43 4423 45 4624 47 4825 49 5026 51 5227 53 5428 55 5629 57 5830 59 6031 61 6232 63 6433 1 2 Partial copy of actual word34 3 435 5 636 7 837 9 1038 11 1239 13 14



Tone Number Bit Number Data Word1 1 2 Actual Word2 3 43 5 64 7 85 9 106 11 127 13 148 15 169 17 1810 19 2011 21 2212 23 2413 25 2614 27 2815 29 3016 31 3217 33 3418 35 3619 37 3820 39 4021 41 4222 43 4423 45 4624 47 4825 49 5026 51 5227 53 5428 55 5629 57 5830 59 6031 61 6232 63 6433 65 6634 67 6835 69 7036 71 7237 73 7438 75 7639 77 78


2.3 Encoding and Decoding

2.3.1 Reed-Solomon Codes

Coding consists of adding redundant bits to the data to be transmitted prior tointerleaving and modulation in order to correct the errors introduced duringtransmission. For the 39 tone signal, the added bits (referred to here as paritybits) are computed using a shortened Reed-Solomon(5,11) block code(RS(5, 11)), whose generator polynomial is

g(x) = x4 + a13x3 + a6x2 + a3x + a10 (1)

The coefficientsai are elements of the binary Galois field of order24 (i.e.,GF (24)). They are formed as the field of polynomials overGF (24) modulo x4 + x + 1 wherex4 + x + 1 is a primitive polynomial.Each 4-bit long symbol mentioned earlier is mapped to an element ofGF (24).

RS codes are block-based error correcting codes. AnRS code is specified asRS(n, k) with s-bit symbols (s = 4 for the 39 tone signal). The term“symbol”used here is different from the 2-bit symbol related to mapping databits to a particular phase. This means that the encoder takesk symbols ofs-bits each and adds parity symbols to create ann-symbol long codeword.There aren− k parity symbols ofs-bits each. AnRS decoder can correct upto t symbols ofs-bits each that contain errors in a codeword, where2t = n− k. The 39 tone signal performs encoding usingRS(7, 3) for bit ratesless than 2400 bps, andRS(14, 10) at 2400 bps. Thus, theRS code cancorrect up to 2 symbol errors. This means that up to 8 bit errors can occur percodeword (either 28 or 56 bits long). More information onRS codes can befound in [2] and [3].

The next several paragraphs provide a brief summary of the Galois theoryrelevant to the calculations for the 39 tone signal.

2.3.2 Galois Fields

A finite field GF (q) has at least one primitive elementa whose order is(q − 1). The nonzero elements of the Galois field are all powers of theprimitive elementa. The elements of a Galois field are closed undermoduloaddition and multiplication. This means that any two elements of the Galoisfield can be multiplied or added to obtain another element of the field.

In the case of the 39 tone signal, the Galois field isGF (24). There are the 16nonzero elements in the Galois field, i.e.,

GF (24) = {0, a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15}


Table 9: Elements of GF (24)

Element ofGF ai modulo (a4 + a + 1) GF (24) Binary Representation(a3, a2, a1, a0)

0 0 0 0 0 0 0a0 1 1 0 0 0 1a1 a a 0 0 1 0a2 a2 a2 0 1 0 0a3 a3 a3 1 0 0 0a4 a4 a + 1 0 0 1 1a5 a2 + a a2 + a 0 1 1 0a6 a3 + a2 a3 + a2 1 1 0 0a7 a4 + a3 a3 + a + 1 1 0 1 1a8 a4 + a2 + 1 a2 + 1 0 1 0 1a9 a3 + a a3 + a 1 0 1 0a10 a4 + a2 a2 + a + 1 0 1 1 1a11 a3 + a2 + a a3 + a2 + a 1 1 1 0a12 a4 + a3 + a2 a3 + a2 + a + 1 1 1 1 1a13 a4 + a3 + a2 + a a3 + a2 + 1 1 1 0 1a14 a4 + a3 + a a3 + 1 1 0 0 1a15 a4 + a 1 0 0 0 1

GF (24) is a binary field, so the coefficients of the elements are 0 and 1. Sinceall arithmetic on the coefficients ismodulo 2, negative signs can be ignored.The elements of the Galois field are defined by taking three initial terms, 0, 1anda, and a primitive polynomial of order 4, (i.e.,q(a) = a4 + a + 1).Starting with 0, 1 anda, the elements ofGF (24) can be found by taking thelast element ofGF , multiplying it by the primitive elementa, and dividing itinto q(a). The process is repeated until the result ofai mod(q(a)) = 1.Table 9 provides the elements ofGF (24).

All operations on the elements of the Galois field are carried out usingmoduloarithmetic, in this casemod(24 − 1). Multiplication is performed as follows:

a13a9 = a(13+9)mod(24−1) = a22mod(15) = a22−15 = a7

Division is performed by multiplying the numerator by the inverse of thedenominator using themodulo operation:

a2/a4 = a2a15−4 = a2+11 = a13

Addition is more complex. Addition is performed by converting the elementto its base representation and adding common terms usingmodulo 2 addition,and then converting the result back to a simple representative element. Forexample,

a5 + a12 = (a2 + a) + (a3 + a2 + a + 1)


= a3 + a2 + a2 + a + a + 1= a3 + 1= a14

Addition of elements ofGF can also be understood by immediately taking theequivalent binary representation, performingmodulo 2 addition, and thenmapping the result to theGF equivalent. For example,

a5 + a12 = (0110) + (1111)= (1001)= a14

2.3.3 RS Encoding

The generator polynomial of anRS code over a Galois field is derived fromthe equation

g(x) = (x + a)(x + a2) · · · (x + a2t). (2)

For2t = n− k (recall thatt = 2 for the 39 tone signal), we have

g(x) = (x + a)(x + a2)(x + a3)(x + a4). (3)

UsingGF (24) arithmetic,

g(x) = x4 + a13x3 + a6x2 + a3x + a10. (4)

An RS(n, k) code takesk symbols and adds(n− k) parity symbols to createann−symbol long message. Consider, for example, theRS(7, 3) code that isused in the 39 tone signal for bit rates below 2400 bps. Letm(x) be themessage to encode. The message will be

t(x) = x2tm(x) + r(x) (5)

wherer(x) = x2tm(x) modulo(g(x)). The termx2t acts as a shift register,placing the original message in the upper bits of the message and adding theparity bits at the end. The result is a coded message that contains the originalmessage. For example, let

m(x) = a1 + a8x1 + a3x2

x2tm(x) = a1x4 + a8x5 + a3x6

and

r(x) = (a1x4 + a8x5 + a3x6) modulo (x4 + a13x3 + a6x2 + a3x + a10)

Using Galois arithmetic,

r(x) = a4x2 + a2x + a8


Then,

t(x) = a3x6 + a8x5 + a1x4 + 0x3 + a4x2 + a2x + a8

Recall that each symbolai represents a 4 bit binary value. Therefore the(7, 3)code in the example above takes3× 4 = 12 message bits, adds4× 4 = 16parity bits, and transmits the resulting 28-bit encoded message. Mapping theGF elements to their binary values (see Table 9) produces the 28-bit longtransmitted message

1000 0101 0010 0000 0011 0100 0101

Similarly, anRS(14, 10) code takes10× 4 = 40 bits and adds4× 4 = 16parity bits, resulting in a 56 bit long message. The 39-tone parallel modeminterleaving function is based on 28-bit codewords. Therefore, a codewordusing theRS(7, 3) code represents one coded message, while theRS(14, 10)code requires two codewords to represent a single coded message.

2.3.4 Decoding RS codes

If v(x) is the received message andt(x) the transmitted message, then

e(x) = v(x)− t(x) (6)

wheree(x) represents the error polynomial, a function of the bit errorsintroduced by the transmission medium. Decoding Reed Solomon codesconsists of determining this error polynomial, and then correcting the receivedword to recover the originally transmitted codeword.

The first step in determining the error polynomial is to determine thesyndromes, the bit patterns used for error-detection and correction [9] , of thereceived message. The syndromes are obtained by reapplying the encodingrules to the received word. To do this, evaluatev(x) at the prescribed roots ofthe generator polynomial{a, a2, a3, · · · , a2t}:

Sj = v(aj), j = 1, · · · , 2t. (7)

Sincet = 2 for theRS(7, 3) andRS(14, 10) used in the 39-tone parallelmode, there will be four syndromes, i.e.,S1, S2, S3 andS4.

The second step consists of determining the error locator polynomialL(x)from the syndrome values where

L(x) = 1 + L1x1 + L2x

2 + · · ·+ Ltxt. (8)

Therefore, fort = 2,

L(x) = 1 + L1x1 + L2x

2. (9)


There are two coefficients,L1 andL2, which, according to [2] and [3], arerelated to the syndrome values through the relation

(S1 S2

S2 S3

)(L2

L1

)=

( −S3−S4

). (10)

From Eq. 10, we obtain

L2 = (S23 − S2S4)/(S2

2 − S1S3) (11)

L1 = (−S22S3 + S1S2S4)/(S3

2 − S1S2S3). (12)

The above equations refer to the situation where two errors are present. Forthis case, the four syndrome values are nonzero. When only one error ispresent,

L1 = S2/S1. (13)

When the four syndromes are null, no bit errors are present and the receivedcode word is identical to the one that had been transmitted. The method usedto find the error locator polynomial is Berlekamp’s iterative algorithmdescribed in [3].

Once the coefficients have been determined, the error locator polynomial mustbe formed and its roots calculated. The roots ofL(x) are the inverses of theerror locators{Xi}, i = 1, · · · , t. To find the roots ofL(x), calculateL(aj)for j = 1, · · · , m− 1, wherem = 2(n−k) − 1. If L(aj) = 0, thenaj is a rootof L(x), andXi = 1/aj , wherei ∈ {1, · · · , t}. For theRS(7, 3) andRS(14, 10) codes, there are only two error locators, sincet = 2.

After the error locators have been calculated, the last step of the decodingprocess, calculating the error polynomial, can be initiated. For that purpose,an infinite degree syndrome polynomial is defined as

S(x) = S1x + S2x2 + · · ·+ S2tx

2t + · · · (14)

The error magnitude polynomial is defined as

O(x) = L(x)(1 + S(x)) modulo (x2t + 1). (15)

The error magnitude polynomial is calculated using the Forney algorithmdescribed in [3]. For theRS(7, 3) andRS(14, 10) codes, the error magnitudepolynomial is

O(x) = (1+L1x1 +L2x

2)(1+S1x1 +S2x

2 +S3x3 +S4x

4) modulo (x5).

Given the error locatorsX1 andX2, the error magnitudes are found to be

Ej1 = O(X−11 )/(1 + X2X

−11 ) (16)


and

Ej2 = O(X−12

)/(a + X1X2X−1). (17)

The error polynomial is then

e(x) = Ej1xj1 + Ej2x

j2 (18)

wherej1 andj2 are the exponents of the error locatorsX1 andX2. Finally,the corrected message, defined ast(x) = v(x) + e(x), should be equal to thetransmitted message, provided no more thant errors were incurred duringtransmission.

2.4 Extracting the Data Bits

In the asynchronous mode of operation, character sets can range between 7 bits and 12bits long. Each of the characters starts with a Start Bit (St) and ends with one or twoStop Bits (Sp), depending on the character set being used. In addition, the charactermay contain a Parity Bit (P). The remaining bits in the character are Data Bits (Da). Forexample, the 10-bit character set used in the Harris AN/PRC-138 radio would bestructured as follows:

St Da Da Da Da Da Da Da P Sp

Prior to American Standard Code for Information Interchange (ASCII) conversion, thedata bits are stripped from the 10-bit word, leaving the 7-bit ASCII character. Thischaracter is then converted to the appropriate symbol using the ASCII conversion table.

As a final point, it should be noted that in synchronous operation the character setscontain only data bits, i.e., there are no start, stop and parity bits.


3. EXPERIMENTAL SET-UP

This section briefly describes the experimental set-up used to collect data samples ofthe 39 tone signal from the Harris AN/PRC-138 manpack radio. The radios weredirectly connected through coaxial cables to the Blackbird system (HP E3238S)([4, 5]). Data collection was performed in the laboratory in a noise and interference freeenvironment. Care was taken to avoid saturation of the A/D converter (HP 1437A). Toprevent saturation, an attenuation of 80 dB was applied to the signal delivered by theHarris radio prior to entering the HP E6500A VXI tuner system of Blackbird. The finalsampling rate of the collected signal was 40 kHz, achieved through the use of thedigital drop receiver in Blackbird. The data was stored in 32 bit complex format. Thecomplex baseband frequency range was -20 kHz to +20 kHz. Using Matlab, thecaptured data file, obtained with a sampling rate of 40 kHz, was resampled to provide anew sampling rate of 14.4 kHz (upsampled by a factor of 9, and downsampled by afactor of 25). Justification for this new sampling rate is discussed later. The resultingdata prior to demodulation and decoding were in the complex baseband frequencyrange of -7200 Hz and +7200 Hz.

For the collections carried out for this study, the radios were operating at a frequency of22 MHz, the upper part of the HF band. As mentioned in [6], the 39 tone signal issupported in the Harris radio in both bit-synchronous and asynchronous modes.Bit-synchronous operation can be done only through the use of what is called theUniversal Data Terminal (UDT) [7]. For the study reported on here, only theasynchronous mode was used.


4. DEMODULATION

This section discusses issues related to synchronization, phase demodulation, and thebit mapping process.

4.1 Synchronization

Prior to continuing with any demodulation processing, it is essential that the signalunder analysis be synchronized in frequency and in time.

The demodulation process is based on the determination of the phase discontinuityoccurring every symbol period between two consecutive signal elements (seeSection 2.2). Phase calculation is the core of the present analysis. For each of the signalelements under analysis, 39 phase values are simultaneously determined. Therefore, adirect phase determination from the imaginary and real part of the time domain signalis not feasible. The signal is decomposed into its frequency components prior toperforming any phase calculation. Consequently, analysis is performed in the frequencydomain. During the analysis, each of the spectral line exactly corresponds to a uniquetone among the tones composing the signal, that is, frequency synchronization isachieved. In other words, a spectral line does not overlap two different tones.

Accurate frequency decomposition of the signal into its components is not enough toensure useful phase demodulation. The determination of each of the phase values usedin the simultaneous demodulation process necessitates spectral analysis over many datapoints of the signal under consideration. To obtain uncorrupted phase values it isessential that the spectral analysis be performed on data sets pertaining to a singlesignal element, that is, the data must be time synchronized. Data sets which overlapcontiguous signal elements will provide phase values unusable for any DQPSKprocessing.

For the present task, the analysis of the signal starts with the beginning of thetransmission. Figure 8 is a time domain representation of the signal. The left side of theplot represents thermal noise occurring before the transmission starts. The right side ofthe plot represents the beginning of the transmission. Parts I and II of the signalpreamble are then available for analysis. It is convenient to use information about thepreamble structure and characteristic to achieve frequency and time synchronization, asdetailed next.

The frequency spectrum of the beginning of the capture is plotted in Figure 9 andshows four unmodulated tones, the first part of the preamble (see Figure 3). Thespectrum was calculated using an 8192 point FFT, and therefore 1.66 Hz bin resolution,with no windowing, over a data segment corresponding to a signal element duration of22.5 ms. Since a sampling rate of 14.4 kHz yields 324 data samples in 22.5 ms,zero-padding was used to increase the number of samples. Once the starting point ofthe transmission has been established, 14 signal elements must be skipped to get to the


0 0.5 1 1.5 2 2.5

−1.5

−1

−0.5

0

0.5

1

1.5

x 10−4

Time (sec)

Am

plitu

de (

V)

Figure 8: Portion of the time domain 39 tone signal.


second part of the preamble, which is characterized by 3 modulated tones. During thissecond part, the phase of the 3 modulated tones is advanced byπ radians from signalelement to signal element. This property was used in our analysis to synchronize thedata in time as follows.

−6000 −4000 −2000 0 2000 4000 6000−150

−140

−130

−120

−110

−100

−90

−80

−708192−point FFT

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

dB/H

z)

Figure 9: Power spectral density of part one of the preamble.

The first step of the process consists of identifying the frequencies of the preambletones. This uses a fine resolution FFT of 1.66 Hz, as discussed above. An example ofthe frequency spectra results for the second part of the preamble is shown in Figure 10.To obtain an accuracy better than 1.66 Hz, a spectral line power- weighted average wasused around the peak positions. The measured frequencies were then compared to thenominal values of the standard [1]. The difference frequency∆f was used to complexmix the captured data to the nominal frequencies.

The second step of the process consists of performing a series of pairs of 256 pointFFT’s over two consecutive signal elements. For a signal sampled at 14.4 kHz, a 256


−6000 −4000 −2000 0 2000 4000 6000−150

−140

−130

−120

−110

−100

−90

−80


Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

dB/H

z)

Figure 10: Power spectral density of part two of the preamble.


point FFT has a resolution of 56.25 Hz which corresponds to the frequency spacing ofthe tones indicated in the standard [1]. If the mixing process has been properly done,each tone in the spectrum will have only one spectral line as shown in Figure 11.

500 1000 1500 2000 2500 3000 3500 40000

2

4

6

8

10

12

14x 10

−7 256−point FFT

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

W/H

z)

Figure 11: Power spectral density of part one of the preamble after frequency synchronization.

In the final step of the process, the real and imaginary parts of the spectral lines areused to calculate a phase value for each 22.5 ms signal element. The resultant phasecalculations for the tones of the first signal element are used to predict what the phasesof the tones should be in the next, or adjacent, signal element. If properly synchronizedin time, the difference between predicted and calculated values should beπ. Thepredicted phase value for the tones of the second signal element is

φn+1 = φn + 2πfT, (19)

wheref is the nominal frequency of one of the tones, andT is the duration of the signalelement (22.5 ms).


The above discussion is based on the ideal situation where the first data point of the 256point FFT block is aligned with the signal element boundary. This will typically not bethe case. More likely the initial 324 point segment to be processed will straddle thesymbol boundary. The steps to be taken to synchronize in time are illustrated inFigure 12. As mentioned above, for a sampling rate of 14.4 kHz, signal elements are324 points long; however, only 256 points of the signal element are used for the FFT.This implies that 68 FFTs must be done by sliding the processed segment positionacross the signal element, one point at a time. For the FFTs associated with blockswithin the symbol period, the phase difference between predicted and calculated valuesshould be tightly distributed aroundπ radians. For the others, where the 256 point FFTsstraddle the symbol boundary, the phase information should be significantly differentfrom π. This effect is illustrated in Figure 13. From this figure, it can be seen that thedata are synchronized in the time range from 0.015 to 0.018 secs. The point in the figurewhere the oscillation is maximum and seems to change polarity corresponds to the casewhere one half of the points (i.e., 128) of the FFT block belong to one symbol period,and the other half to the adjacent symbol period. These observations are corroboratedby the spectra illustrated in Figures 14, 15 and 16. Figure 14 corresponds to the casewhen time synchronization has been achieved, and the other two when it has not.


Beginning of Transmission

22.5 ms ( 324 Samples)

Beginning of Acquisition (arbitrary)

N th symbol period

Time (sec.)

Symbol Boundary

Symbol Boundary

324 Samples (22.5 ms)

256 Sample FFT 256 Sample FFT

324 Samples (22.5 ms)

324 Samples (22.5 ms) 324 Samples (22.5 ms)

Symbol Boundary

Symbol Boundary

256 Sample FFT 256 Sample FFT

Figure 12: Time synchronization process.


0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 0.0222.8

2.9

3

3.1

3.2

3.3

3.4

Time(sec)

Pha

se D

iffer

ence

(R

adia

ns)

Figure 13: Phase difference during time synchronization process.


−6000 −4000 −2000 0 2000 4000 6000

−105

−100

−95

−90

−85

−80

−75

−70

−65

−60

−55


Frequency (Hz)

Pow

er S

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ty (

dB/H

z)

Figure 14: Spectrum when data are synchronized in time.


−6000 −4000 −2000 0 2000 4000 6000−105

−100

−95

−90

−85

−80

−75

−70

−65


Frequency (Hz)

Pow

er S

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dB/H

z)

Figure 15: Spectrum when time synchronization is not perfectly achieved.


−6000 −4000 −2000 0 2000 4000 6000−105

−100

−95

−90

−85

−80

−75

−70

−65


Frequency (Hz)

Pow

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dB/H

z)

Figure 16: Spectrum when there is no time synchronization whatsoever.


4.2 Phase Demodulation

Once synchronization has been achieved, the phase demodulation process can begin.The data signal elements corresponding to the first two parts of the preamble can beskipped, and demodulation can start at the block synchronization part of the frame (seeFigure 3).

Before carrying out any processing, the frequencies of the tones must be checked and,if necessary, corrected of any shift that may have occurred during the transmission. TheDoppler tone is monitored for this purpose. The frequency synchronization processdescribed above is repeated here, using the 8192 point FFT with zero padding over onesignal element. An example of the spectrum is illustrated in Figure 17. An accurateposition of the Doppler peak is determined by a power-weighted average and thefrequency difference between this value and the nominal value from the standard(393.75 Hz) is calculated. This difference is used in a complex mixing operation toshift the time-synchronized complex data to the nominal value.

−6000 −4000 −2000 0 2000 4000 6000−180

−170

−160

−150

−140

−130

−120

−110

−100

−90


Frequency (Hz)

Pow

er S

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ty (

dB/H

z)

Figure 17: Spectrum of 39 tone waveform.


The Harris radios generate their 39 tone signals in the digital domain, prior to D/Aconversion, using a 7.2 kHz sampling rate. At the receiving end, they sample theincoming signal at 14.4 kHz. Doubling the sampling rate on reception produces twointerleaved blocks of 128 points each at a sampling rate of 7.2 kHz. Performing128-point FFT’s (56.25 Hz resolution) on each of the data blocks provides a snapshotof the phase behavior of the tones during a sampling interval. This additionalinformation is used to refine the DQPSK demodulation process.

After frequency and time synchronization have been achieved, a 128-point FFT of adeinterleaved subblock of the 256 block is performed within a signal element. The FFTresults are shown in Figure 18. Each of the 39 tones (not including the Doppler tone)corresponds to only one spectral line, each having an amplitude and phase. Theamplitudes of the tones are within the tolerance indicated in the standard. Also, theseparation of the spectral lines allows comparison of phases from one symbol period toanother. From the measurements that were carried out, it was observed that the signalfrom the radio oscillated in frequency, with a range of±8 Hz over a duration ofapproximately 1 second. The Doppler tone was monitored, and its frequency used tocorrect for any frequency and phase offsets from tone to tone. Finally, by calculatingtwo deinterleaved 128-point FFTs per signal element, the phase variation from signalelement to signal element for each of the 39 tones could be monitored and used to makerefinements. Figure 19 shows a bar chart of the phase differences observed for tonenumber one over time. There are four distinct average phase levels. These levels,however, do not correspond to the values mentioned in the standard.

Figure 20 shows the phase differences for tone one, over 703 signal elements, presentedin the form of a polar plot or constellation diagram. The phases cluster into four areas90 degrees apart, with each cluster spread over 30 to 40 degrees around a centroid. Theconstellation for tone number 10 is illustrated in Figure 21. Its centroid is offset fromthat for tone number one. It was found that the clusters for the various tones were offsetfrom one another in a progressive manner by about -5.5 degrees, suggesting that therewas a frequency rotation occurring across the tones. It was hypothesized that thisrotation was due to an offset in the spacing of the 39 tones. This offset may haveoriginated from a lack of performance in the transmitter while maintaining the tonefrequencies within the values specified in [1]. It may also have been created by thesampling rate of the Blackbird equipment. A combination of these circumstances couldalso have caused the offset. Unfortunately, time did not permit looking for ways toremedy this offset. However, it was still possible to demodulate the signal and convertthe symbols into di-bits, albeit with some effort.

First, the constellations must be rotated into place so that the clusters are centered at 45,135, 225, and 315 degrees. Rotating the constellation for a particular tone involves anambiguity of 90, 180, or 270 degrees. This is the case for each tone. To determine thecorrect rotational value, di-bits were generated for various rotational values. Then thebit pattern in the block synchronization part of the frame and the redundancycharacteristics in the message were sought. Two of the 39 correctly rotated


−3000 −2000 −1000 0 1000 2000 3000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

−8 128−point FFT

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

W/H

z)

Figure 18: Spectrum of 39 tone waveform after time and frequency synchronization.


5 10 15 20 25 300

50

100

150

200

250

300

350

400

Pha

se D

iffer

ence

(de

gree

s)

Signal Element Number

Figure 19: Successive phase differences from symbol period to symbol period for tone number 1 over a duration of

30 symbol periods.


0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

Figure 20: Signal constellation for tone number one over 703 symbol periods.


0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

Figure 21: Signal constellation for tone number 10 over 703 symbol periods.


constellations are illustrated in Figures 22 and 23.

0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

Figure 22: Signal constellation for tone number one over 703 symbol periods after constellation rotation.

Once rotated, the phases could be mapped to di-bits according to the values shown inFigure 5. For each signal element, a 78-bit long stream is built. To verify the validity ofthe bit stream obtained, the redundancy patterns mentioned in Tables 3 to 7 wereidentified. The first pattern occurs when bits 65 to 78 are redundant with bits 1 to 14.The second redundancy pattern applies to bits of consecutive signal elements for datarates below 1200 bps. For example, for 75 bps, bits 1 to 4 constitute the actual datawords, while bits 5 to 8 are redundant with the data word transmitted one signalelement in the past. Once the redundancy is successfully identified, the redundant bitsare removed from the bit stream in order to obtain the decodable bit stream. A finalcheck consists of identifying the final bits of the framing sequence which, according to[1], is 1111111110 (see Figure 24). The sequence repeats according to the insertion


0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

Figure 23: Signal constellation for tone number 10 over 703 symbol periods after constellation rotation.


interval and framing sequence length values indicated in Table 2. For the 10-bitcharacter set used in this study and a long interleaving degree (e.g. 585, see Table 2), a16380-bit long insertion interval and a 260-bit long framing sequence were found to beused. Therefore, the 1111111110 sequence repeats every 16640 bits. This result wasfound while analyzing the 1200 bit rate mode.

90 100 110 120 130 140 150 160 170−1

−0.5

0

0.5

1

1.5

2

Bit Number

Bit

Val

ue

End Sequence

Data SuperblockFraming Sequence

Figure 24: End sequence for first framing sequence


5. DEINTERLEAVING AND DECODING

The deinterleaving and decoding process is summarized in Figure 25. Thedeinterleaving process is based on a series of Matlab developed algorithms. The use ofthese algorithms requires input ofa priori knowledge of both the bit rate andinterleaving degree. The bit rate can be deduced from analyzing the redundancy levelsdescribed earlier. Thus, for a given bit rate, the deinterleaving degree can be obtainedthrough the tracing of two consecutive framing sequences. The number of bits betweenthe two 1111111110 sequences can be determined and the interleaving degree lookedup in a table. The deinterleaving process is carried out as described in the followingparagraphs.

First, based on tabulated values extracted from [1], the synchronization sequence length(framing sequence) in numbers of bits and insertion interval in numbers of superblocks,is determined for a given bit rate and interleaving degree.

Second, based on the identification of the final bits of two consecutive framingsequences, the data superblocks are identified and extracted from the decodable bitstream. The identification of the framing sequence is accomplished by matching 10-bitlong sequences extracted from the decodable bit stream with the end sequence1111111110. The end sequence indicates where the framing sequence ends and wherethe data superblocks start. After the first end sequence is found, its repeat interval isverified against intervals specified in [1]. The interval, in numbers of bits, between twoconsecutive end sequences corresponds to the number of bits contained in all thesuperblocks. For the 10-bit character and the 1200 bps asynchronous mode discussedhere, the number of bits is 16380, with a framing sequence of 260 bits. Thus, twoconsecutive end sequences are 16640 bits apart in the decodable bit stream. When thetwo conditions described above are satisfied, the data superblocks are extracted fromthe decodable bit stream.

Third, the deinterleaving operation is initiated. According to [1], deinterleaving isperformed on each individual superblock, and there can be several superblocks betweenthe framing sequences. Therefore, the number of superblocks must be known. Thisinformation is also in [1] and depends on the bit rate and interleaving degree. Thenumber of codewords in a superblock is also needed to perform deinterleaving. Thisnumber depends on the interleaving degree, and, from Table 2, the interleaving degreecould be understood to be the number of codewords in a superblock.

Recall that a codeword is either 28 or 56 bits long. The portion of the bit streamcorresponding to the insertion interval is partitioned in segments whose length, given inbits, is 4 times the number of codewords (recall that each symbol is 4 bits long). Thenumber of segments so obtained corresponds to the number of symbols composing thecodewords (7 for bits rates below 2400 bps and 14 for 2400 bps). The segments arethen stacked in a 7 or 14 row matrix as illustrated in Figures 6 and 7. This stackingoperation allows isolating each of the codewords.


Block Sync

Super Block

Super Block

Block Sync

Super Block

4 bits x Interleaving Degree 1

Note: Interleaving degree is equivalent to # of Codewords

DS 1 DS 2

Stack

DS 3 DS 4

DS 1 DS 2

DS 3 DS 4

DS 5 DS 6

PS 1

PS 2

PS 3

PS 4

PS 5

PS 6

PS 7

PS 8

DS is a Data Code Symbol Equal to 4 bits

PS is a Parity Code Symbol Equal to 4 bits

1.0

2.0

CW 1 CW 2

CW is a Code Word Equal to 28 bits

3.0

DS 1 DS 2

DS 3 DS 4

DS 5 DS 6

Decode to DS 1 DS 3 and DS 5 ( bit correction and removal of parity bits )

Decode to DS 2 DS 4 and DS 6

Deinterleave

DS 1 DS 3 DS 5 DS 2 DS 6 DS 4

Partition into 10 bit long characters

DS 1 DS 2 DS 3 DS 5 DS 6 DS 4

10 10 10 10

St Sp Sp Da Da Da Da Da Da Da

Extract 7 bit ASCII Character Start Bit = 0 Stop Bits = 0

Figure 25: Deinterleaving and decoding process.


The final operation consists of reorganizing the bit stream so that all the bits of eachcodeword are in continuous sequence, starting with the first codeword of thesuperblock. The deinterleaving process is illustrated in Figure 25 for the 1200 bps datarate, with an interleaving degree of 585 (1 superblock per insertion interval, 585codewords per superblock, 12 data bits and 16 parity bits per codeword). Thisdeinterleaving process is repeated for all the superblocks in the insertion interval.

Decoding is performed, in sequence, over the deinterleaved bit stream of each of thecodewords pertaining to the same superblock. That is, decode the bit stream ofcodeword 1, then of codeword 2, and so on.

The decoding is done by calls to a series of Matlab functions. One function calculatesthe syndromes of the codeword, or received polynomial. Another, based onBerlekamp’s iterative algorithm, determines the error locator polynomial from thesyndrome values. This is followed by a function that calculates the roots of the errorlocator polynomial to obtain the error locators. The last Matlab function, based onForney’s algorithm, calculates the error magnitude polynomial.

The above operations determine the error pattern in the received codeword and,therefore, allow one to retrieve the transmitted codeword. This operation is repeated forall codewords of the same superblock.

The resulting bit stream now contains only data bits, all parity bits having beenremoved. Since during the encoding process codewords were created in pairs andtherefore interleaved, another deinterleaving operation must be carried out. (Refer toFigures 6 and 7 for odd and even numbers of codewords.) In the case of an odd numberof codewords in the superblock, the last codeword in the superblock does not belong toa pair of codewords and, therefore, has not been interleaved.

After this last deinterleaving operation has been carried out, the original transmitted bitstream is recovered. For synchronous transmission, the decoded bit stream is split into7-bit long characters and ASCII conversion is performed. For asynchronoustransmission, the decoded bit stream is split into segments corresponding to the numberof bits forming the characters (10-bit characters for this study). The start bit, stop bitand parity bit are removed ([1] indicates that these are zero or null bits) and the 7-bitlong ASCII characters are formed. This is illustrated in the following example:

Step 1:Extract the decoded bit stream.000010110000000010000001101100011110110000111011000111001100

Step 2:Split the bit stream into 10-bit long characters.0000101100 0000001000 0001101100 0111101100 00111011000111001100

Step 3:Remove the start bit at the beginning of each character, as well as thestop bit and parity bit at the end, to obtain the 7-bit ASCII characters.


000101100000100011011111101101110111110011

Step 4:Perform ASCII conversion, as in Table 10. The bits must be reversedinside each 7-bit long character before performing ASCII conversion.

Table 10: Example of Decoded Bit Stream

Binary String Decimal Value Character1101111 111 o1110110 118 v1100101 101 e1110010 114 r0001101 13 carriage return0001010 10 line feed1110011 115 s1110101 117 u1100011 99 c1101000 104 h0100000 32 space1101100 108 l1101111 111 o1101110 110 n1100111 103 g


6. CONCLUSIONS

The work presented in this report summarizes the familiarization activity in receiving,demodulating and decoding a 39 tone signal. This work consisted of obtaining a strongunderstanding of this type of signal and in reaching a stable point in the development ofthe algorithms. It was possible to retrieve the content of a message intercepted in alaboratory environment. However, the problem of the rotation in the constellationsrequires more research. It was speculated (but not proven) that this rotation probablyresulted from the tones not being exactly spaced 56.25 Hz apart as specified in [1].

The signal captures were carried out in an ideal laboratory situation. The currentalgorithms must be enhanced to be able to handle the more general situation. Presently,time synchronization of the data, prior to demodulation, is based on the preamble tones.As mentioned in the report, a signal reception can occur anywhere during thetransmission. If this is the case, any of the 39 tones can be used for timesynchronization purposes. This added capability in the algorithms will require only aslight modification. Another problem with the general intercept case is thata prioriknowledge of some parameters were used for the deinterleaving and decoding activities(i.e., bit rate and interleaving degree). Bit rate can be easily identified by looking at theredundancy within one signal element (for 2400 and 1200 bps) and from theredundancy pattern existing between subsequent signal elements for bit rates below1200 bps. Once the bit rate has been identified, the interleaving degree can be deducedby determining the length in bits of the insertion interval (between framing sequencebits 1111111110). Finally, the decoding algorithms must improved to be able to handlethe 2400 bps case, which uses 56-bit codewords.


References

1. Department of Defense, USA,“Interoperability and Performance Standards forData Modem MIL-STD-188-110A”, September, 1991

2. Plank, J. S., “A Tutorial on Reed-Solomon Coding for Fault-Tolerance inRAID-like Systems”, Technical Report UT-CS-96-332, Department of ComputerScience, University of Tennessee, July, 1996

3. Michelson, A. M., Levesque, A. H., “Error Control Techniques for DigitalCommunication”, John Wiley and Sons Inc., 1985

4. Hewlett Packard, “HP E6500A VXI Tuner User’s Guide”, Hewlett PackardPublication E6500-90001, November, 1997

5. Hewlett Packard, “HP E6501A/E6502A/E6503A VXI Receiver User’s Guide”,Hewlett Packard Publication E6500-90006, September, 1998

6. Harris, “Falcon Series Tactical Communications System AN/PRC-138 ManpackInstallation and Operation Manual”, Harris Publication 10372-0008-01, November,1993

7. Harris, “RF-6710 Universal Data Terminal (UDT) Software User’s Guide”, HarrisPublication 10518-2020-01, February, 1997

8. Harris, “RT-1694 Receiver-Transmitter Intermediate Maintenance Manual”, HarrisPublication 10515-0007-4300, Rev. A, December, 1995

9. “Comprehensive Dictionary of Electrical Engineering”, P.A. Laylante, editor, CRCPress, IEEE Press, 1999


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1. ORIGINATOR (the name and address of the organization preparing the document. Organizations for whom the document was prepared, e.g. Establishment sponsoring a contractor’s report, or tasking agency, are entered in section 8.)

DEFENCE R&D CANADA - OTTAWA OTTAWA, ONTARIO, K1A 0Z4

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including special warning terms if applicable) UNCLASSIFIED

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DEMODULATION AND DECODING STUDIES OF THE 39-TONE MIL-STD-188-110A HF SIGNAL (U)

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DUPRAT, GERARD.

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NOVEMBER 2002

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(U) AA sseett ooff aallggoorriitthhmmss hhaass bbeeeenn ddeevveellooppeedd ttoo ddeemmoodduullaattee aanndd ddeeccooddee tthhee 3399 ttoonnee ssiiggnnaall,, wwhhiicchh iiss pprreevvaalleenntt iinn tthhee HHiigghh FFrreeqquueennccyy ((HHFF)) ffrreeqquueennccyy bbaanndd.. TThhiiss ssiiggnnaall,, bbaasseedd oonn tthhee MMIILL--SSTTDD--118888--111100AA SSttaannddaarrdd,, iiss oonnee ooff sseevveerraall ddiiffffeerreenntt ttyyppeess ggeenneerraatteedd bbyy tthhee AANN//PPRRCC--113388 HHaarrrriiss rraaddiioo.. DDeeffeennccee RR&&DD CCaannaaddaa ((DDRRDDCC)) -- OOttttaawwaa hhaass ttwwoo ooff tthheessee rraaddiiooss.. TThhee wwoorrkk ffooccuusseedd oonn tthhee 3399 ttoonnee ffiixxeedd ffrreeqquueennccyy mmooddee,, aalltthhoouugghh tthhee 3399 ttoonnee ssiiggnnaall iiss aallssoo tthhee uunnddeerrllyyiinngg mmoodduullaattiioonn uusseedd iinn tthhee AANN//PPRRCC--113388''ss ffrreeqquueennccyy hhooppppiinngg mmooddee.. TThhuuss,, tthhee wwoorrkk ddeessccrriibbeedd hheerree wwiillll aallssoo bbee uusseeffuull ttoo aannyyoonnee ddeevveellooppiinngg ddeehhooppppiinngg aanndd ddeemmoodduullaattiioonn aallggoorriitthhmmss ffoorr tthhee AANN//PPRRCC--113388 ffrreeqquueennccyy hhooppppiinngg ssiiggnnaall.. TThhee ssiiggnnaallss wweerree ccaappttuurreedd bbyy tthhee AAggiilleenntt TTeecchhnnoollooggiieess BBllaacckkbbiirrdd ssyysstteemm iinn aa llaabboorraattoorryy sseettttiinngg.. TThhee oobbjjeeccttiivvee ooff tthhee ttaasskk wwaass ttoo ggaaiinn aa ddeettaaiilleedd uunnddeerrssttaannddiinngg ooff tthhee ssoopphhiissttiiccaatteedd 3399 ttoonnee ssiiggnnaall aanndd ttoo ddeevveelloopp ssooffttwwaarree rraaddiioo aallggoorriitthhmmss ffoorr ddeemmoodduullaattiinngg aanndd ddeeccooddiinngg tthhee ssiiggnnaall.. TThhee rreeppoorrtt ddeessccrriibbeess tthhee ssiiggnnaall ssttrruuccttuurree,, tthhee ssiiggnnaall ccaappttuurree eeqquuiippmmeenntt,, aanndd tthhee sstteeppss iinnvvoollvveedd iinn ddeemmoodduullaattiinngg aanndd ddeeccooddiinngg tthhee ssiiggnnaall ssoo tthhaatt tthhee ttrraannssmmiitttteedd mmeessssaaggeess ccaann bbee rreeaadd aatt tthhee rreecceeiivviinngg eenndd.. TThhee rreeppoorrtt aallssoo ddeessccrriibbeess tthhee pprroobblleemmss eennccoouunntteerreedd dduurriinngg tthhee aallggoorriitthhmm ddeevveellooppmmeenntt pprroocceessss.. SSiinnccee tthhee ssiiggnnaall ccaappttuurreess ttooookk ppllaaccee iinn aann iiddeeaall sseettttiinngg aanndd aa pprriioorrii iinnffoorrmmaattiioonn ooff tthhee ssiiggnnaall ssttrruuccttuurree wwaass uusseedd ttoo aassssiisstt iinn tthhee ddeemmoodduullaattiioonn aanndd ddeeccooddiinngg pprroocceessss,, tthhee ccuurrrreenntt aallggoorriitthhmmss mmuusstt bbee mmooddiiffiieedd sslliigghhttllyy ttoo bbee aabbllee ttoo hhaannddllee tthhee mmoorree ggeenneerraall ssiittuuaattiioonn.. TThhee rreeppoorrtt ccoonncclluuddeess wwiitthh wwaayyss ooff ggeenneerraalliizziinngg tthhee aallggoorriitthhmmss..

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39 TONE MIL-STD-188-110A RADIO FREQUENCY COMMUNICATIONS HF DQPSK REED-SOLOMON GALOIS FIELD ENCODING/DECODING SIGNAL DEMODULATION

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